**Authors**

**Abstract**

Ground vibrations during an earthquake can severely damage structures and equipments housed in them. Many factors including earthquake magnitude, distance from the fault or epicenter, duration of strong shaking, soil condition of the site, and the frequency content of the motion define the properties of ground motion and its amplification. A deep understanding of the effects of these factors on the response of structures and equipments is essential for a safe and economical design. Some of these effects such as the amplitude of the motion, frequency content, and local soil conditions are best represented through a response spectrum, which describes the maximum response of a damped single-degree-of-freedom (SDOF) oscillator with various frequencies or periods to ground motion.

Earthquake ground motion is usually measured by strong motion instruments, which record the acceleration of the ground. The recorded accelerograms, after corrections for instrument errors and baseline, are integrated to obtain the velocity and displacement time-histories.

The maximum response of a SDOF system excited at its base by a time acceleration function is expressed in terms of only three parameters: (1) the natural frequency of the system, (2) the amount of damping, and (3) the acceleration time-history of the ground motion. Response spectrum analysis is the dominant contemporary method for dynamic analysis of building structures under seismic loading. The main reasons for the widespread use of this method are: its relative simplicity, its inherent conservatism, and its applicability to elastic analysis of complex systems. Since the detailed characteristics of future earthquakes are not known, the majority of earthquake design spectra are obtained by weighted averaging of a set of response spectra from records with similar characteristics such as soil condition, epicentral distance, magnitude and source mechanism.

The design spectrum specifies the design seismic acceleration, velocity or displacement at a given frequency or period if it is derived from ground acceleration, velocity or displacement time histories. For practical applications, design spectra are presented as smooth curves or straight lines. Smoothing is carried out to eliminate the peaks and valleys in the response spectra that are not desirable for design because of the difficulties encountered in determining the exact frequencies and mode shapes of structures during severe earthquakes when the structural behavior is most likely nonlinear. Since the peak ground acceleration, velocity, and displacement for various earthquake records are different, the computed response cannot be averaged on an absolute basis. Thus, normalization is needed to make a standard basis for averaging. Various procedures are used to normalize the response spectra before averaging is carried out. Among these procedures, one has been the most commonly used, which is normalization with respect to peak ground motion to make the same peak ground motion for all ground motion time histories.

Building codes commonly present design spectra in terms of acceleration amplification as a function of period on an arithmetic scale. In this study, the data from Accelerographic network stations are deployed on rock sites of Iran with shear wave velocity larger than 750 m/s, which is equivalent to site Type I in the Iranian seismic building code. The Seismosignal software is used to do both baseline correction and filtering for all the dominant horizontal and vertical components to reduce the inherent error of the motion. Among all the ground motions, only 103 vertical and 109 dominant horizontal time histories are accepted after baseline correction and filtering. The data are classified considering different combinations of the range of magnitude and distance. The epicentral distance is classified as near field (0-35 km), medium distance (35-65 km) and far field (65-100 km), while the earthquake magnitude is classified as small earthquake (4.5<M<5.5), medium earthquake (5.5<M<6.5) and large earthquake (6.5<M<7.5), after which the vertical and the horizontal response spectra are prepared for each time history for %5 damping ratio. Obviously, the result can be generalized to other damping ratios. By averaging the response spectra is obtained an unsmoothed design spectra. A smoothed design spectra is plotted by averaging of acceleration amplification spectra for each frequency. This procedure is repeated for an average plus one standard deviation of both vertical and horizontal response spectra.

Eventually, the smoothed design spectra determined in this study are compared with that of the regional attenuation relationships obtained based on the data from Europe and the Middle East (Ambraseys et al., 2005). The comparisons show relatively good correlation between the spectrum obtained in this study and the regional attenuation relationships for periods greater than about 0.19sand weak correlation for periods of less than it.

Earthquake ground motion is usually measured by strong motion instruments, which record the acceleration of the ground. The recorded accelerograms, after corrections for instrument errors and baseline, are integrated to obtain the velocity and displacement time-histories.

The maximum response of a SDOF system excited at its base by a time acceleration function is expressed in terms of only three parameters: (1) the natural frequency of the system, (2) the amount of damping, and (3) the acceleration time-history of the ground motion. Response spectrum analysis is the dominant contemporary method for dynamic analysis of building structures under seismic loading. The main reasons for the widespread use of this method are: its relative simplicity, its inherent conservatism, and its applicability to elastic analysis of complex systems. Since the detailed characteristics of future earthquakes are not known, the majority of earthquake design spectra are obtained by weighted averaging of a set of response spectra from records with similar characteristics such as soil condition, epicentral distance, magnitude and source mechanism.

The design spectrum specifies the design seismic acceleration, velocity or displacement at a given frequency or period if it is derived from ground acceleration, velocity or displacement time histories. For practical applications, design spectra are presented as smooth curves or straight lines. Smoothing is carried out to eliminate the peaks and valleys in the response spectra that are not desirable for design because of the difficulties encountered in determining the exact frequencies and mode shapes of structures during severe earthquakes when the structural behavior is most likely nonlinear. Since the peak ground acceleration, velocity, and displacement for various earthquake records are different, the computed response cannot be averaged on an absolute basis. Thus, normalization is needed to make a standard basis for averaging. Various procedures are used to normalize the response spectra before averaging is carried out. Among these procedures, one has been the most commonly used, which is normalization with respect to peak ground motion to make the same peak ground motion for all ground motion time histories.

Building codes commonly present design spectra in terms of acceleration amplification as a function of period on an arithmetic scale. In this study, the data from Accelerographic network stations are deployed on rock sites of Iran with shear wave velocity larger than 750 m/s, which is equivalent to site Type I in the Iranian seismic building code. The Seismosignal software is used to do both baseline correction and filtering for all the dominant horizontal and vertical components to reduce the inherent error of the motion. Among all the ground motions, only 103 vertical and 109 dominant horizontal time histories are accepted after baseline correction and filtering. The data are classified considering different combinations of the range of magnitude and distance. The epicentral distance is classified as near field (0-35 km), medium distance (35-65 km) and far field (65-100 km), while the earthquake magnitude is classified as small earthquake (4.5<M<5.5), medium earthquake (5.5<M<6.5) and large earthquake (6.5<M<7.5), after which the vertical and the horizontal response spectra are prepared for each time history for %5 damping ratio. Obviously, the result can be generalized to other damping ratios. By averaging the response spectra is obtained an unsmoothed design spectra. A smoothed design spectra is plotted by averaging of acceleration amplification spectra for each frequency. This procedure is repeated for an average plus one standard deviation of both vertical and horizontal response spectra.

Eventually, the smoothed design spectra determined in this study are compared with that of the regional attenuation relationships obtained based on the data from Europe and the Middle East (Ambraseys et al., 2005). The comparisons show relatively good correlation between the spectrum obtained in this study and the regional attenuation relationships for periods greater than about 0.19sand weak correlation for periods of less than it.

**Keywords**